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Dynamics of an impulsive control system which prey species share a common predator

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  • Yongzhen, Pei
  • Yong, Yang
  • Changguo, Li

Abstract

In an ecosystem multiple prey species often share a common predator and the interactions between the preys are neutral. In view of these facts and based on a multiple species prey–predator system with Holling IV and II functional responses, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is proved that there exists a locally asymptotically stable pest-eradication periodic solution under the assumption that the impulsive period is less than some critical value (or the release amount of the predator is greater than another critical value). Permanence conditions are established when the impulsive period is greater than another critical value (or the release amount of the predator is less than some critical value). Numerical results show that the system we consider has more complex dynamics including period solution, quasi-periodic oscillation, chaos, intermittency and crises.

Suggested Citation

  • Yongzhen, Pei & Yong, Yang & Changguo, Li, 2009. "Dynamics of an impulsive control system which prey species share a common predator," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2429-2436.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2429-2436
    DOI: 10.1016/j.chaos.2008.09.016
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    References listed on IDEAS

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    1. Zhang, Shuwen & Chen, Lansun, 2005. "A Holling II functional response food chain model with impulsive perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1269-1278.
    2. Zhang, Shuwen & Wang, Fengyan & Chen, Lansun, 2005. "A food chain model with impulsive perturbations and Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 855-866.
    3. Zhang, Shuwen & Tan, Dejun & Chen, Lansun, 2006. "Dynamic complexities of a food chain model with impulsive perturbations and Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 768-777.
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